"We haven't yet evaluated how successful those reforms will be. I at least would be interested in seeing whether or not those are successful before rendering a final judgment."

Mr Cameron's visit to Washington comes against a backdrop of fevered debate within the Conservative Party over Britain's relations with the EU, with a potentially divisive vote expected in the House of Commons on Wednesday over whether the Government's agenda for this year should include a bill to pave the way for an in/out referendum.

Two Cabinet ministers - Education Secretary Michael Gove and Defence Secretary Philip Hammond - have said they would vote for a British exit if a referendum were held now.

Two ministerial aides, Conservative MPs Stuart Andrew and Gavin Barwell, said they will back the rebel amendment on Wednesday, after Downing Street took the highly unusually step of indicating that Parliamentary Private Secretaries (PPSs) will be allowed to do so without losing their jobs. Tory ministers have been told they may abstain, but cannot back the amendment, which has been signed by more than 50 backbenchers.

Speaking at a press conference following his talks with Mr Obama, Mr Cameron insisted that a referendum now would not be in the national interest, as voters would be presented with a "false choice" between an unreformed EU or British exit.

He stressed the potential benefits for the UK of a mooted free trade deal between the EU and US, which he said could be worth up to £10 billion a year to Britain.

The Prime Minister said: "Everything I do in this area is guided by a very simple principle, which is what is in the national interests of Britain?

"Is it in the national interests of Britain to have a trans-Atlantic trade deal that will make our countries more prosperous, that will get people to work, that will help our businesses? Yes it is, and so we will push for this trans-Atlantic trade deal.

"Is it in our interests to reform the European Union, to make it more open, more competitive, more flexible, and to improve Britain's place within the European Union? Yes, it is in our national interests.

"And it's not only in our national interest, it is achievable because Europe has to change because the single currency is driving change for that part of the European Union that is in the single currency. Just as they want changes, so I believe Britain is quite entitled to ask for and to get changes in response.

"Finally, is it in Britain's national interest once we have achieved those changes, but before the end of 2017, to consult the British public in a proper, full-on in/out referendum? Yes, I believe it is.

"That's the approach that we take. Everything driven by what is in the British national interest. That is what I'm going to deliver. It's absolutely right for our country. It has very strong support throughout the country and in the Conservative Party and that's exactly what I'm going to do."

The proposed free trade deal between the European Union and the US was high on the agenda at the White House talks, one in a series of discussions with leaders of the world's biggest economic powers ahead of next month's G8 summit in Lough Erne, Northern Ireland.

Mr Cameron said: "President Obama and I have both championed a free trade deal between the European Union and the United States, and there's a real chance now to get the process launched in time for the G8.

"The next five weeks are crucial. To realise the huge benefits this deal could bring will take ambition and political will. That means everything on the table - even the difficult issues - and no exceptions.

"It's worth the effort. For Britain alone, an ambitious deal could be worth up £10 billion a year, boosting industries from car manufacturing to financial services."

Earlier this year, Mr Obama told the Prime Minister that the US "values a strong UK in a strong European Union", in comments which were widely interpreted as an indication of concern in Washington that Britain was heading towards withdrawal.

Today, the President said: "With respect to the relationship between the UK and the EU, we have a special relationship with the United Kingdom and we believe that our capacity to partner with a United Kingdom that is active, robust, outward-looking and engaged with the world is hugely important to our own interests, as well as the world.

"I think the UK's participation in the EU is an expression of its influence and its role in the world as well as obviously a very important economic partnership.

"Ultimately, the people of the UK have to make decisions for themselves."